Preheat the oven to 350°F and line 2 large baking sheets with parchment paper.
In a large bowl, beat 1 cup softened butter and granulated sugar with a mixer on medium speed for 2 minutes until very light and fluffy.
Add the egg and 2 teaspoons vanilla bean paste and beat until smooth and glossy, scraping down the sides of the bowl.
In a separate bowl, whisk together the flour, baking soda, baking powder, and 1/2 teaspoon salt.
Add the dry ingredients to the butter mixture on low speed and mix just until a thick, soft dough forms with no dry flour remaining.
Add the 2 tablespoons milk and mix on low until fully incorporated and the dough is smooth.
Divide the dough into 5 equal portions and place each portion in a small bowl.
Tint each portion with a small amount of gel food coloring, kneading gently until the color is evenly distributed and pastel.
Scoop tablespoon sized portions of dough and roll each into a smooth ball between your palms.
Arrange the dough balls on the prepared baking sheets, spacing them 2 inches apart.
Bake one sheet at a time for 9 to 11 minutes, until the edges look set and the tops are no longer shiny but the centers are still soft.
Let the cookies cool on the baking sheets for 5 minutes, then transfer them to a wire rack to cool completely.
While the cookies cool, make the filling by beating 1/2 cup softened butter in a medium bowl until creamy.
Add the powdered sugar, 1 teaspoon vanilla bean paste, pinch of salt, and 2 tablespoons heavy cream or milk.
Beat on low speed until combined, then on medium speed until thick, smooth, and spreadable.
If the filling is too thick, add a few drops of cream or milk; if it is too thin, beat in a little more powdered sugar until it holds its shape.
Once the cookies are completely cool, pair them by size and color, placing one cookie of each pair flat side up.
Pipe or spread about 1 tablespoon of filling onto the flat side of each bottom cookie.
Top each with a second cookie, flat side down, and gently press and twist until the filling spreads to the edges.
Let the cookie sandwiches sit at room temperature for 10 minutes to allow the filling to firm before serving.